Towering centre-forward Carroll was purchased from Liverpool for £15million after a successful season-long loan at Upton Park last term whilst winger Downing was also bought from Liverpool this summer for around £5m.
Allardyce sees the pair as being a potential answer to his goalscoring worries after the Hammers netted the least goals of all the top 10 clubs last season.
"To pick up two players of the quality of Stewart and Andy is good business both financially and in football terms, and they will help to improve us as an attacking unit," he told the club's official website.
"Stewart is a great player with a very good pedigree. If you look at his technical and physical stats, it puts him right up there among the top players we have at the club.
"He's a talented boy with good energy, and will improve the team quality, particularly in possession. He doesn't give the ball away, he can hold it if he needs to and he can dribble as well.
"Stewart will be able to produce the kind of ball we need, and will have the opportunity to cross the ball, just as he did at Aston Villa."